# Cosmology and thermodynamics

1. Aug 9, 2011

### TrickyDicky

Since the second law of thermodynamics builds upon the first, if the first law doesn't apply to cosmology like it keeps being repeated around here, it would seem to follow that that the second law doesn't apply either.
Could this be clarified by someone tat actually knows about cosmology (like Chalnoth or bapowell)?

2. Aug 9, 2011

### Staff: Mentor

What about the 1st law doesn't apply to cosmology?

3. Aug 9, 2011

### bcrowell

Staff Emeritus

Why would it follow?

The first law doesn't apply. The second law does.

4. Aug 10, 2011

### Chalnoth

The second law of thermodynamics is generally understood today to be a fundamental rule based upon simple probability: systems tend towards more probable configurations with time. This really isn't a rule that you can get rid of.

5. Aug 10, 2011

### TrickyDicky

Hmm, doesn't the second law rely on the existence of an invariant quantity (energy) to postulate another quantity that increases whenever there is flow from Work to Heat?.
Such a process implies time.
As the energy-time uncertainty principle shows, to measure energy variation a unidirectional passage of time is needed. The variation of heat (dQ) produced in such process fulfills at all times the first law dU=dQ+dW in order for the quantity dS=dQ/T to hold, and also for the non-usable work to end up increasing the internal energy of the system (adiabatic process) or also the internal energy of the surroundings of the system:T$\Delta S_u$ .

This is not contradicted by the "more probable configuration" view of entropy. Why would you consider the firs law an easier law to get rid than the second if thay are both two sides of the same coin?

It is precisely nature's strife to keep with energy conservation book-keeping that ensures that all processes that involve time as a parameter tend to the more probable configuration (the one that keeps energy constant).
As this seems quite basic thermodynamics stuff, I would think that if there's an error in what I wrote it'll be easily spotted and indicated. It seems necessary to straighten this out in order to go back to the issue in cosmology.

6. Aug 10, 2011

### Staff: Mentor

I don't see how energy NOT being conserved has any affect on whether or not systems will tend towards a more probable configuration.

7. Aug 10, 2011

### TrickyDicky

Because if energy wasn't conserved, that is if energy could be created or destroyed and therefore perpetuum mobiles were possible, no configuration would be more probable than others, no gradients or potentials would need to be minimized so energy is conserved since no gradients would form (remember energy is free if it is not conserved), there couldn't be an absolute scale of temperature (no zeroth law) either.
If you are curious as to why once there is energy conservation systems tend to the more probable configuration (since in this case configurations have different probabilities) that is purely semantic, the laws of thermodynamics give you a direction arrow, then we simply call the end point of the arrow "more probable" and the beginning of the arrow less probable, it wouldn't make any difference for the physics if we named them the other way around.

8. Aug 10, 2011

### bcrowell

Staff Emeritus
No, you can just define entropy in terms of the number of accessible states.

Huh? I don't see how any of this has anything to do with quantum-mechanics. We don't have a theory of quantum gravity, so we can't even discuss this quantum-mechanically.

There is no big mystery or controversy about any of this. The first law doesn't hold, and the second law is typically believed to hold. You don't have to trust me on this. For the statement that the first law fails, see the cosmology FAQ entry I linked to above and the references therein. The validity of the second law is pretty much universally assumed, as you can see from even a casual look at the literature. So if you think there is some trivial contradiction there, then you clearly are disagreeing with every cosmologist in the business. It's great if you want to ask probing questions about the conventional wisdom in the field, but if you're proposing that the conventional wisdom is wrong for trivial reasons, then the outcome is going to be that you're going to learn why your reasons are wrong, because people working in the field are not morons.

9. Aug 10, 2011

### TrickyDicky

Certainly, and as I explained the fact that in an isolated system in which a thermodynamic constrain is removed has more accessible states can be explained in terms of conservation of the internal energy of the system.

I specified in a previous post that it would be interesting to clarify first the thermodynamical issue of the inseparability of the thermodynamics laws. If this is not the place to discuss it, I'm open to move it to other subforums.
I hope you'll agree there is a theory of quantum thermodynamics.
Obviously I'm not proposing such thing but your mentioning it leads me to suspect you are just avoiding the physical issue.

10. Aug 10, 2011

### Staff: Mentor

I see no reason that most of this should be true. In my view using my limited knowledge of the subject, a system in equilibium with another system that suddenly acquires more energy would still tend to evolve towards the new equilibrium. Your view seems to be based on the 2nd law NOT being true.

11. Aug 10, 2011

### Chalnoth

The "number of microstates" view is completely independent of considerations related to energy.

12. Aug 11, 2011

### TrickyDicky

So you keep repeating but without further clarification it is either misleading or wrong.
If what you mean is that absolute entropy of a system at a given time is dependent only on the probability of the microstates, without energy entering the formula, that's correct.
Note that absolute entropy at a given time doesn't inform us about the process in time nor gives any unidirectional flow or dynamical picture wich is the core of the second law.
And microstates don't come out of the blue, they have a physical meaning. Besides a probability of being occupied they have an energy. And the mean of the sistem's energy is the internal energy wich must be conserved in order to measure non negative variation of entropy in spontaneous proccesses.

13. Aug 11, 2011

### Chalnoth

While it is true that you can decrease the entropy of a system by pumping energy into it, non-decreasing entropy is still taken to be more fundamental than energy conservation.

Quantum effects, like the ones you mentioned, do not impact this argument because they tend to average out, producing no net change in energy.

Gravity is more difficult to factor in, because gravity breaks the assumptions that go into classical thermodynamics. So the relationships we make use of in thermodynamics are not expected to hold except in special cases where the gravitational entropy is either negligible or isn't changing. Furthermore, energy isn't always conserved in General Relativity (it is conserved in special cases).

14. Aug 11, 2011

### TrickyDicky

Why? They're both parts of the same process, I don't understand why one is taken to be more fundamental than the other.
It's like saying that in the sales process of a product is more fundamental the buying than the selling, it is just dependent on whose POV is used , the buyer's or the seller's.
Instead of entropy we could equally choose to use Free-energy=internal energy-unusable ($T\Delta S$) energy, wich is a form of using an energy dynamic measure (free energy decreases the same way entropy increases) for instance when using Gibbs or Helmholtz free energy.
According to WP : "Free energy is that portion of any first-law energy that is available to perform thermodynamic work; i.e., work mediated by thermal energy. Free energy is subject to irreversible loss in the course of such work. Since first-law energy is always conserved, it is evident that free energy is an expendable, second-law kind of energy that can perform work within finite amounts of time."
It is evident from this that the second and first law are inextricably interconnected, it makes little sense considering one more fundamental than the other except for special applications.
And makes no sense at all to claim one law holds and the other doesn't, since they are each based on the other holding true.

Sure, in an equilibrium situation there is no net change of internal energy, this follows from the first law too.

15. Aug 11, 2011

### TrickyDicky

Back to cosmology, judging by the answers I'm getting, it seems clear a choice has been made by "working cosmologists" (and according to the references provided), that when faced between thermodynamics as a logically complete model with all of its laws, and the FLRW model of cosmology as put forward in the 30's of the XXth century , they clearly lean towards the latter.
I guess that is a valid choice if sufficiently supported, but not the only choice possible.
What I don't understand is what kind of arbitrarines allows to cherry pick certain laws of thermodynamics and not others ignoring that thermodynamics is a logically complete whole that includes all of their laws.

16. Aug 11, 2011

### Chalnoth

Because entropy is simply related to the number of microstates that can replicate a given macrostate. This means that the second law of thermodynamics is, fundamentally, a statement about probability: systems tend towards higher-probability states.

If you look carefully at what the heat transfer part means in classical thermodynamics you see that this condition is what is required to ensure that global entropy increases. In other words, the heat transfer part of the second law of thermodynamics is peculiar to the classical assumptions used.

Out of equilibrium as well. Quantum effects simply don't lead to average changes in energy.

17. Aug 13, 2011

### TrickyDicky

I'm still not sure whether you consider energy conservation a necessary condition for the second law.
Let's consider as usual isolated systems (the universe is normally considered an isolated system) and it might be useful to differentiate reversible processes from irreversible ones.
So if we consider an isolated system far from equilibrium we have the irreversible case and there is unidirectional time and the second law that states that it'll tend towards more probable configurations with time until it reaches equilibrium.
What happens to the system if we don't impose that dU=0 (first law)? Basically that energy can be created within the system to avoid the gradient that is formed far from equilibrium, IOW an artificial equilibrium can be formed that prevents any more probable configuration to tend to and therefore there is never increase in entropy and dS=0.

Is this wrong?

18. Aug 13, 2011

### Chalnoth

The part of the second law of thermodynamics that relates to how a transfer of heat can allow a decrease in entropy assumes energy conservation from the start. If you don't have energy conservation, then this part of the second law would have to be rewritten to take that into account when you have an open system.

However, if I just want to deal with a lack of conservation of energy and don't want to worry too much about how that impacts the behavior of open systems, I can just take a closed system and be sure that the entropy won't decrease. Once the system is closed, the conservation or non-conservation of energy is completely irrelevant. Energy conservation only comes into it when you want to understand the behavior of an open system.

19. Aug 13, 2011

### TrickyDicky

That part of the second law is the only part as it is usually defined.

I'm not sure if you are using the standard meaning of "closed system" in thermodynamics (a system that can exchange energy but not matter). In such a sytem entropy can decrease (like in a refrigerator), remain invariant if no net energy is transfered or increase.
Do you mean that once equilibrium is reached conservation of energy is irrelevant? The fact is all isolated systems in equilibrium trivially conserve energy (they are reversible systems and time symmetric by definition).

To make things simpler and since the universe is considered an isolated system and also most definitions of entropy are made in terms of isolated systems I suggest we stick to isolated systems.

20. Aug 13, 2011

### Chalnoth

Looking it up, I suppose the more accurate term is an isolated system, which has no interaction with the outside world. A refrigerator obviously interacts with the outside world, and couldn't work if it didn't.